Structural system utilizing membrane structural panels having double ruled quadric surfaces

ABSTRACT

A BASIC STRUCTURAL ELEMENT IS FORMED FROM A WARPED MEMBRANE STRUCTURAL PANEL HAVING DOUBLE RULED QUADRIC SURFACES. THE DOUBLE RULED QUARDIC SURFACES OF THE PANEL HAVE BIAXIALLY ORIENTED SURFACE RULINGS, THE EDGES OF A PREFERRED EMBODIMENT OF THE PANEL LYING IN PLANES PARALLEL TO ONE OR THE OTHER OF THE SETS OF RULINGS. THE MEMBRANE PANEL HAS FOUR EDGES, PAIRS OF WHICH ARE EQUAL IN LENGTH. IN SOME CASE, THE WARPED PANEL MAY BE ENCLOSED IN A PANEL SURFACED TETRAHEDRAL ENVELOPE, THE EDGES OF THE PLANE SURFACES BEING JOINED TO THE EDGES OF THE ENCLOSED WARPED SURFACES. BASIC STRUCTURAL ELEMENTS FORMED BY THE WARPED MEMBRANE PANELS, EITHER BY THEMSELVES OR IN COMBINATION WITH THE PLANE SURFACED TETRAHEDRAL ENVELOPE, MAY BE ADDED TOGETHER TO FORM VARIOUS COMPOSITE MODULES WHICH CAN BE FURTHER INTEGRATED TO CREATE STRUCTURES USEFUL AS PANELS, POSTS, BEAMS, AND THE LIKE.

March 9, 1971 J. R. HALE 3,563,331

STRUCTURAL ST UTIL NG M RANE STRUCTURAL PANELS H NG UBLE LED DRIC SURFACES Filed Nov. 27, 1968 4 Sheets-Sheet 1 JEssE 2. HALE ex aaak 454/ 14 TTOQA/VS March 9, 1971 J. R. HALE 3,555,381 I STRUCTURAL SYSTEM LIZING MEMBRANE STRUCTURAL PANELS HAVING DO E RULED QUADRIC SURFACES Filed Nov. 27, 1968 4 Sheets-Sheet 2 WVEA/TQQ JessE i2. HALE HALE 3,568,381 MEMBRANE STRUCTURAL PANELS QUADRIC SURFACES March 9, 1971 J. R.

STRUCTURAL SYSTEM UTILIZII\G HAVING DOUBLE RULED Filed Nov. 2'7, 1968 4 Sheets-Sheet 5 /A/VEA/T02. Jesse l2. HALE BY M 9 60W ATTOEMFVS FIG. 14

March 9, 1971 J, E 3,568,381

sT ucTpRAL SYSTEM UTILIZING MEMBRANE STRUCTURAL PANELS HAVING DOUBLE RULED QUADRIC SURFACES Filed NOV. 2'7, 1968 4 Sheets-Sheet 4.

M/VEA/TOZ. pw L/ JESSE IZHALE- esmzhduw United States Patent ()fice 3,568,381 Patented Mar. 9, 1971 3,568,381 STRUCTURAL SYSTEM UTILIZING MEM- BRANE STRUCTURAL PANELS HAVING DOUBLE RULED QUADRIC SURFACES Jesse R. Hale, 14020 Budlong Ave., Gardena, Calif. 90247 Filed Nov. 27, 1968, Ser. No. 785,851

Int. Cl. E04b 1/32, 7/10 US. C]. 5281 12 Claims ABSTRACT OF THE DISCLOSURE A basic structural element is formed from a Warped membrane structural panel having double ruled quadric surfaces. The double ruled quadric surfaces of the panel have biaxially oriented surface rulings, the edges of a preferred embodiment of the panel lying in planes parallel to one or the other of the sets of rulings. The membrane panel has four edges, pairs of which are equal in length. In some cases, the warped panel may be enclosed in a plane surfaced tetrahedral envelope, the edges of the plane surfaces being joined to the edges of the enclosed warped surfaces. Basic structural elements formed by the warped membrane panels, either by themselves or in combination with the plane surfaced tetrahedral envelope, may be added together to form various composite modules which can be further integrated to create structures useful as panels, posts, beams, and the like.

This invention relates to structural elements, and more particularly to such elements comprising warped surface panels which may be integrated to form such structures as panels, posts, and beams.

In the design of structural panels, cores for structural panels, posts and beams, the principal consideration is to create the maximum moment of inertia possible, to impart to the structure both integrity and rigidity. There are many situations such as, for example, the fabrication of aircraft structures, where a high strength-to-weight ratio is essential. Material such as thermoformed plastics are relatively light Weight and economical to fabricate, but have inherently poor physical properties for structural applications.

The fabrication of structural elements having high structural integrity and rigidity from materials such as thermoformed plashtics by forming such material into a membrane structure having double ruled quadric surfaces is described in my co-pending application, Ser. No. 741,- 600 filed July 1, 1968. The structures of this invention utilize the basic advantages of membranes having double ruled quadric surfaces in a basic double ruled membrane structural panel element which may be enclosed in a tetrahedral plane surfaced enveloped (which could be provided by surface panels where the elements are used as the core material of a sandwich structure) or may be used as a basic structural element without such an envelope.

The basic structural elements of this invention may be joined together to form structural modules which in turn may be combined to form integrated structures, such as posts, beams and panels. A plurality of the basic structural elements of the invention can be combined together to form an optimum structure capable of handling all normal stresses. This optimum structure can be degenerated by the removal of unnecessary structural elements into lesser structures for handling specific stress patterns, as dictated by application requirements. Thus, sufficient structural integrity provided without the weight penalty and cost of the optimum design in situations where such optimum design is not required. The device of this invention thus provides basic building block structural elements which can be utilized to fabricate an integrated structure having optimum characteristics for the particular application requirements at hand.

It is therefore the principal object of this invention to provide an improved modular structural system having optimum rigidity and structural integrity and which may utilize light weight material such as thermoformed plastics which have inherently low rigidity, as well as conventional structural materials.

The invention will now be described in connection with the accompanying drawings of which:

FIG. 1a is a perspective view of a first basic structural element of the device of the invention.

FIG. 1b is an elevational view of the structural element of FIG. 1a, taken along the plane indicated by lb-lb in FIG. 10,

FIG. 10 is a side elevational view of the element of FIG. 1a,

FIG. 1d is a top plan view taken along the plane indicated by 1d-1d in FIG. 1b,

FIG. 2a is a perspective view of a structural module integrated from three of the basic elements illustrated in FIGS. 1a1d,

FIG. 2b is a top plan view of the structural module of FIG. 2a,

FIG. 3 is a perspective view illustrating a cubical module which represents the integration of eight of the structural modules of FIGS. 2a, 2b,

FIG. 4a is an elevational view of a second basic structural element of the device of the invention,

FIG. 4b is a view taken along the plane indicated by 4b4b in FIG. 4a,

FIG. 4c is a view taken along the plane indicated by 4c4c in FIG. 4a,

FIG. 5 is a perspective view illustrating a structural module representing the integration of four of the structural elements of FIGS. 4a-4c,

FIG. 6 is a perspective view illustrating how the structural module of FIG. 5 may be utilized in combination with the structures of FIG. 3 in forming a post, beam, panel or other structures,

FIGS. 7a and 7b illustrate a structural module formed from six of the membrane panels of FIG. 1,

FIGS. 8a and 8b illustrate a structural module formed from four of the membrane panel units of FIGS. la-ld,

FIG. 9 illustrates a structural module formed from four of the membrane panels of FIGS. 1a1d,

FIGS. 10a and 10b illustrate a structural module formed by combining a module of the type illustrated in FIG. 9 with a module formed from two of the membrane structures of FIGS. 4a 4c,

FIGS. 11a and 11b illustrate a structural module formed by combining the module of FIGS. 8a and 8b with the module formed from a pair of membrane panels of FIGS. 4a4c,

FIG. 12 illustrates a structural module formed from eight of the membrane panels of FIGS. la-ld,

FIG. 13 illustrates the formation of a structural module by combining the module of FIG. 9 with that of FIG. 12,

FIG. 14 illustrates a structural module formed from twenty-four of the membrane panels of the embodiment of FIGS. la1c,

FIG. 15 illustrates a cubical structural module formed from a plurality of membrane panels of the embodiment of FIGS. 4a-4d, and

FIG. 16 illustrates how the module of FIG. 14 may be utilized in combination with modules of the type illustrated in FIG. 15.

Briefly described, the structural element of this invention comprises a membrane which has a double ruled surface, such surface being quadric, in the form of a hyperbolic paraboloid. The membrane has four edges, pairs of which are equal in length and in a preferred embodiment, opposite edges of which are located in planes parallel to one of the sets of the biaxially oriented rulings. In certain embodiments of the invention, the membrane panel is enveloped by a plane surfaced tetrahedron, the edges of sides of the tetrahedron extending along and being joined to the edges of the warped membrane, the rulings of the warped surface thus being oriented to create trusses with the plane surfaces of the tetrahedron which act as chordal elements. Where the structural elements form the core material of a sandwich panel, the plane surfaced envelope may be at least partially formed by the panel elements. In one embodiment of the basic structural element of the invention, the length of each of the pairs of equal length membrane edges is diiferent, while in another embodiment, all four edges are equal. A plurality of the basic structural elements of the invention may be combined in various configurations to form structural modules which may be integrated into structures having optimum capabilities for various application requirements.

Referring now to FIGS. la-ld, a first embodiment of the basic structural element of the invention is illustrated. Membrane panel 11 which may be formed from a suitable material such as a sheet of metal or plastic, has a hyperbolic paraboloid surface which is defined as a double ruled quadric surface. A first set of such rulings are represented by lines 12 (drawn on the surface of the sheet for convenience of illustration) while a second set of such rulings are indicated by lines 13, rulings 12 being oriented orthogonal to edges 15a and rulings 13 being orthogonal to edges 1511. A first pair of edges 15a and 15b, which bound membrane panel 11, are equal in length, and a second pair of membrane panel edges 16a and 16b are equal in length, the length of these pairs being different. Opposite edges 15a and 16a lie in planes parallel to rulings 13 while opposite edges 15b and 16b lie in planes parallel to rulings 12.

Membrane 11 is enclosed in a' plane surfaced envelope 17 which forms a tetrahedron. The sides of tetrahedron 17 are triangular, two of the edges (17a-17h) of each side corresponding to an edge of membrane 11 to which it is joined. The third edge of each side of the tetrahedron is joined to an edge of an adjacent side of the tetrahedron where these edges meet at 171' and 17k. The composite element formed is thus a double ruled quadric surface panel enclosed within a plane surfaced tetrahedron envelope.

Referring now to FIGS. 2a and 2b, a structural module formed from three of the structural elements of FIGS. la1d is illustrated. Three structural elements 19 of the type shown in FIGS. *la-ld are joined together along their edges. The integrated structure 20 thus formed has an outer hexahedron envelope. As for the basic structural element of FIGS. lald, the faces of the hexahedron are triangular with two of the edges of each side corresponding to and joined with an associated edge of one of the membrane panels 11, and the third edge of each side joined to an edge of an adjacent side where the two meet.

Referring now to FIG. 3, the integration of eight of the modules of FIGS. 2a and 2b into a cubic structural member is illustrated. Structural modules 20 are joined together at their edges to form a cube having pyramidal recesses 22 on each of the six faces thereof. A plurality of the units of FIG. 3 can be joined toegther to form an integrated matrix structure for various application requirements or can be combined with structural modules of the type illustrated in FIG. (as described further on in the specification in connection with FIG. 6).

Referring now to FIGS. 4a4c, a second embodiment of the basic structural element of the invention is illustrated. This second embodiment is similar in configuration to the first embodiment described in connection with FIGS. la-ld, except for the fact that all of the four edges 4 15a, 15b, 16a and 16b are equal rather than only two pairs thereof. The membrane panel 11a, as for the first embodiment, is enclosed within a plane surfaced tetraheldron envelope 17 which runs along the edges of the membrane, the warped surface becoming a structural median of the envelope.

Referring now to FIG. 5, a structural module 30 cOnstructed from four structural elements of the type shown in FIGS. 4a-4c is shown. The integrated structure thus formed has a plane surfaced octahedron envelope. As for the previous embodiments, the edges of the double ruled quadric surfaces 11 join with two corresponding edges of each of the sides of their envelopes 17 with the third edges of each of these sides joining with a corresponding edge on an adjacent side thereof. The module of FIG. 5 corresponds to the analog octahedon of crystallography. A plurality of modules 30 can be combined to form an integral matrix structure suitable for various application requirements.

Referring now to FIG. 6, the utilization of modules 30 in combination with a plurality of cubic structures of the type described in connection with FIG. 3 is illustrated. As seen in the figure, structural modules 30 fit into recesses 22 in cubic structural members 21. The structure formed by this combination represents the optimum structural matrix capable of carrying all of the normal stresses at maximum etficiency.

Referring now to FIGS. 7a and 7b, a modular configuration consisting of six of the double ruled quadric surfaced membrane panels of the type described in connection with FIGS. la-ld is shown. In forming this module, the longer pairs of equal edges 16a and 16b of the six membrane panels 11 are joined together with the shorter edge pairs 15a and 15b forming the side and bottom edges of he module. A plurality of such modules formed in sheet material makes for excellent core structure since the ridges terminating the module (along edges 16b) can be oriented in the core structure parallel to each other or normal to each other without changing the structural values of the core. When the ridges are parallel, gases can be readily passed through the core with very little pressure drop. Two sheets containing an adjoined plurality of these nodes can be stacked ridge to ridge, with the ridges normal to each other in a second case, thus creating a very small area of contact. This arrangement allows the 45 elements of the structure to continue from one face sheet to the other in straight lines to offer maximum resistance to bending in a sandwich paenl with minimum heat transfer.

Referring now to FIGS. 8a and 8b, a structural module formed from four of the membrane panel units as described in connection with FIGS. lald is illustrated. In this embodiment, one of the longer edges 16b of each of the membrane panels 11 forms each of the sides of the square base of the module, while the other of the longer edges 16a are joined to an adjacent membrane unit, with one of the shorter edges 15a of each of the units being joined to another of the units to form the top ridge of the structure; the others of the shorter edges 15b being joined together to form the side edges of the structure. This module thus has a square base and terminates in a ridge similar to that of the module described in connection with FIG. 7a and 7b. A plurality of the modules of FIGS. 8a and 8b can be joined together at their square bases with half of the ridges running normal to the other half, thus creating an isotropic pattern.

Referring now to FIG. 9, an embodiment of the invention utilizing four of the membrane panel units of FIG. 1 arranged about a square base is illustrated. This module is formed by synthesizing four of the membrane panels of FIG. 1 into a square based module having an apex 35. The four membrane sections are arranged side by side with their longer edges 16a and 16b abutting each other, and with their shorter edges 15a and 15b forming the base of the module. A multiplicity of this module can of course be formed with suitable punches and dies from a single sheet of plastic and need not be made by integrating four separate membrane panels 11.

Referring now to FIGS. a and 10b, a structural module which is synthesized by combining the module of FIG. 9 with pairs of the membrane panels of FIG. 4a-4c is illustrated. Pairs of membrane panel units 11a are joined together along two of their edges a and 15b, the remaining edges of the membrane 16a and 16b forming the square base of the module. The modules formed from the membrane panels 11a are joined to the modules formed from the membranes 11 along the joinder edges of the membranes, the integrated structures having the base portion of one module facing an opposite direction to that of another.

Referring now to FIGS. 11a and 11b, a further structural module is illustrated, this module being formed by reinforcing the module of FIGS. 8a and 8b with a pair of membrane panels of the embodiment of FIGS. 4a'-4c. As can be seen, a pair of the membrane panels 11a as described in connection with FIGS. 4a-4c, are joined together along their edges to form a square based unit and this unit is attached along its base in internal concentricity with the unit formed from four membrane panels 11, as shown in FIGS. 8a and 8b.

Referring now to FIG. 12, a further modular structure is illustrated, this structure being synthesized from eight membrane panel units 11 of the type described in connection with FIGS. 1alc. The membrane units 11, as can be seen in the figure, are joined together along their longer edges 16a and 16b, the joinder edges 16b forming four ridges which are normal to each other. The square base of the module is formed by one of the shorter edges 15a of the membrane panel.

Referring now to FIG. 13, the synthesis of a modular structure of the type illustrated in FIG. 9 with a structure of the type illustrated in FIG. 12 is illustrated. As can be seen, in synthesizing the two modules, the module of FIG. 9 is nested within that of FIG. 12, with the base portions of the two modules formed by edge portions 15a, 15b, 16b and 17 being joined together.

Referring now to FIG. 14, a cubical modular structure formed from 24 membrane panels of the type shown in FIGS. la-ld is illustrated. This structure is similar in configuration to that shown in FIG. 3 except for the fact that it is formed solely from membrane elements 11 and does not include any plane surfaced envelope surrounding such membranes.

Referring now to FIG. 15, a structural module representing the integration of four of the membrane panel elements of the embodiment of FIGS. 4a-4c is illustrated. This embodiment is similar to that illustrated in FIG. 5, except for the face that it only includes membrane elements 11a and does not include a plane surfaced envelope enclosing such membrane elements.

Referring now to FIG. 16, the utilization of structural modules of the type illustrated in FIG. 15 in combination with elements of the type illustrated in FIG. 14 is illustrated. The elements 30a thus fit within the recesses 22a of the cubical modules 21a in the same general manner as described in connection with FIG. 6 for the similar structural modules having plane surfacedenvelopes.

It should be apparent that many other combinations of the basic elements of this invention and the modules already described can be made to form various structures for particular application requirements. It is to be noted that a synthesis of the basic elements of the invention as shown, for example, in FIG. 6 represents an optimum structure for handling all types of loads. This optimum structure, however, in the interest of saving cost and weight, can be degenerated down into structures having a lesser number of basic structural elements to forms which are suitable for particular application requirements not necessitating the optimum structure. Thus, this invention involves basic structural elements which can be synthesized to form various structural modules which in turn can be combined to form structural units for various application requirements.

I claim:

1. A structural module formed from six structural elements, each of said elements comprising a membrane panel having a double ruled quadric surface, said membrane panel being bounded by a first pair of equal edges and a second pair of equal edges longer than said first pair, said edges lying in planes parallel to the rulings of said surface, said membrane panels being joined to each other at said longer edges, said second pairs of edges forming a square base of said module, two pairs of said edges forming a ridge running opposite said base between a pair of corners thereof.

2. A structural module formed from four structural elements, each of said elements comprising a membrane panel having a double ruled quadric surface, said panel being bounded by a first pair of equal edges and a second pair of equal edges longer than said first pair, said edges lying in planes parallel to the rulings of said surface, said elements being joined together at said first pair of edges and one of the longer of said edges, the others of the longer of said edges forming a square base of said module, said first pairs of edges forming a ridge of said module running opposite said base between opposite corners thereof.

3. The structural module of claim 2 and additionally comprising a peaked reinforcing member having a square base placed in internal concentricity with said module, the base of said member being adjacent to the base of the module, said reinforcing member including a pair of membrane panels having double ruled quadric surfaces bounded by four equal edges, two of the edges of said pair of panels being joined together, the other edges of the aforesaid panels forming the base portion of said member.

4. A structural module comprising three similar four edged membrane panels joined together along similar edges thereof to form an integral three sided unit, each of said panels having a double ruled quadric surface bounded by a first pair of equal edges and a second pair of equal edges, two of the edges of a first one of said panels each being respectively joined to a corresponding edge of a second one of said panels, the third of said panels interconnecting the first and second panels with two of the edges thereof joined to corresponding edges of said first panel and the other two edges thereof joined to corresponding edges of said second panel.

5. The structure of claim 4 and further including a plane surfaced hexahedron envelope enclosing said panels, two of the edges of each of the sides of said hexahedron coextending with and joined to corresponding edges of said panels.

6. A structural module comprising eight similar membrane panels joined together to form a unit having a square base and four ridges normal to each other,

each panel having a double ruled quadric surface bounded by a first pair of equal edges and a second pair of equal edges larger than said first pair, said edges each lying in a plane parallel to an associated set of rulings of said surface,

the longer edges of each of said panels each being joined to a longer edge of another of said panels, four of the joinder lines of said longer edges forming said four ridges,

said base being formed by one of the shorter edges of each of said panels.

7. A structural module comprising:

a plurality of similar membrane panel elements, each such element having a double ruled quadric surface bounded by a first pair of equal edges and a second pair of equal edges, said edges each lying in a plane parallel to an associated set of rulings of said surface,

a first structural unit formed from four pairs of said panel elements, the elements forming each such pair being joined together along two of the edges thereof to form a peaked unit having a square base, the base portions of said pairs being joined together to form a square based unit,

a second structural unit formed from four of said elements joined together along two of the edges thereof, the remaining edges forming a square base, the joined together edges extending from the base and terminating in an apex above the center of the base,

said first and second structural units being joined together along the joinder edges of the membrane elements thereof, with the base portions of said units facing in opposite directions to one another.

8. A structural module comprising eight similar modules joined together along the edges thereof to form a cubic structure having recesses in each of the sides thereof, each of said eight modules comprising:

three similar four edged membrane panels joined together along similar edges thereof to form an integral three sided unit,

each of said panels having a double ruled quadric surface bounded by a first pair of equal edges and a second pair of equal edges, two of the edges of a first one of said panels each being respectively joined to a corresponding edge of a second one of said panels, the third of said panels interconnecting the first and second panels with two of the edges thereof joined to corresponding edges of said first panel and the other two edges thereof joined to corresponding edges of said second panel.

9. A structural-module comprising eight modules joined together along the edges thereof to form a cubic structure having pyramidal recesses in each of the sides thereof, each of said eight modules comprising:

three similar four edged membrane panels joined togetheralong similar edges thereof to form an integral three sided unit,

each of said panels having a double ruled quadric surface bounded by a first pair of equal edges anda second pair of equal edges, two of the edges of a first one of said panels each being respectively joined to a corresponding edge of a second one of said panels, the third of said panels interconnecting the first andsecond panels with two of the edges thereof joined to corresponding edges of said first panel and the other two edges thereof joined to corresponding edges of said second panel, and plane surfaced hexahedron envelope enclosing each of said eight modules, two of the edges of each of the sides of the hexahedron coextending with and joined to corresponding edges of said panels.

10. In combination, a pair of structural modules each comprising eight similar modules joined together along the edge thereof to form a cubic structure having recesses in each of the sides thereof and a third structural module integrated with said pair of modules, said third module comprising four membrane panels having double ruled quadric surfaces and each bounded by four equal edges, said panels being joined together at their edges to form a. four sided symmetrical unit, said third module being fitted into the recesses of a side of each of said pair of modules, each of said eight modules comprising:

three similar four edged membrane panels joined together along similar edges thereof to form an integral three sided unit,

each of said panels having a double ruled quadric surface bounded by a first pair of equal edges and a second pair of equal edges, two of the edges of a first one of said panels each being respectively joined to a corresponding edge of a second one of said panels, the third of said panels interconnecting the first and second panels with two of the edges thereof joined to corresponding edges of said first panel and 8 the other two edges thereof joined to corresponding edges of said second panel.

11. In combination, a pair of structural modules each comprising eight modules joined together along the edges thereof to form a cubic structure having pyramidal recesses in each of the sides thereof, and a third structural module integrated with said pair of modules, said third module comprising four membrane panels having double ruled quadric surfaces and each bonded by four equal edges, said panels being joined together at their edges to form a four sided symmetrical unit, said unit being enclosed in a plane surfaced octahedron envelope, said third module being fitted into the recesses of a side of each of said pair of modules, each of said eight modules comprising:

three similar four edged membrane panels joined to gether along similar edges thereof to form an integral three sided unit, each of said panels having a double ruled quadric surface bounded by a first pair of equal edges and a second pair of equal edges, two of the edges of a first one of said panels each being respectively joined to a corresponding edge of a second one of said panels, the third of said panels interconnecting the first and second panels with two of the edges thereof joined to corresponding edges of said first panel and the other two edges thereof joined to corresponding edges of said second panel, and plane surfaced hexahedron envelope enclosing each of said eight modules, two of the edges of each of the sides of the hexahedron coextending with and joined to corresponding edges of said panels. 12. In combination, a structural module comprising eight similar membrane panels joined together to form a unit having a square base and four ridges normal to each other and a second structural module formed from four of said membrane panels joined together along the longer edges thereof, the shorter edges thereof forming a square base with the longer edges extending from said base and terminating in an apex above the center of said base, said second module being nested within the first mentioned module, the bases of said modules being joined together, each panel having a double ruled quadric surface bounded by a first pair of equal edges and a second pair of equal edges larger than said first pair, said edges each lying in a plane parallel to an associated set of rulings of said surface,

the longer edges of each of said panels each being joined to a longer edge of another of said panels, four of the joinder lines of said longer edges forming said four ridges,

said base being formed by one of the shorter edges of each of said panels.

References Cited UNITED STATES PATENTS 2,839,841 6/1958 Berry 3572 2,891,491 6/1959 Ruhter 528l 3,092,932 6/1963 Wilson 5280 3,094,812 6/1963 Peeler 52-80 3,206,895 9/1965 De Ridder 528() FOREIGN PATENTS 1,120,195 1956 France 528O 1,230,904 1960 France 5280 OTHER REFERENCES Mathematical Models, by Candy and Rollett, Oxford University Press, 1961, pp. 168, 169, 176187, and 192- HENRY C. SUTHERLAND, Primary Examiner US. 01. X.R. 52-575 

